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The Hilbert-Smith conjecture states, for any connected topological manifold $M$, any locally compact subgroup of $\mathrm{Homeo}(M)$ is a Lie group. We generalize basic results of Segal-Kosniowski-tomDieck (2.6), James-Segal (2.12), G…

Geometric Topology · Mathematics 2022-02-23 Qayum Khan

We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie…

Quantum Algebra · Mathematics 2024-04-02 Saeid Azam , Amir Farahmand Parsa

A compact K\"ahler manifold is shown to be simply-connected if its `symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective…

Algebraic Geometry · Mathematics 2015-11-06 Yohan Brunebarbe , Frédéric Campana

The semidirect product $\mathbb{G}=\mathbb{L}\rtimes \mathbb{K}$ attached to a compact-group action on a connected, simply-connected solvable Lie group has a dense set of compact elements precisely when the $s\in \mathbb{K}$ operating on…

Group Theory · Mathematics 2025-07-08 Alexandru Chirvasitu

We present an explicit construction of the basic bundle gerbes with connection over all connected compact simple Lie groups. These are geometric objects that appear naturally in the Lagrangian approach to the WZW conformal field theories.…

Differential Geometry · Mathematics 2009-11-10 Krzysztof Gawedzki , Nuno Reis

Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations $\overline{\rho}$ of the Lie group $\mathrm{Diff}_c(M)$ of compactly supported diffeomorphisms of a smooth manifold $M$ that…

Mathematical Physics · Physics 2025-01-29 Bas Janssens , Milan Niestijl

In this paper, we completely classify three-dimensional Lorentzian $Ein(2)$ Lie groups.

Differential Geometry · Mathematics 2020-07-28 Yong Wang

The purpose of this paper is to consider some basic constructions in the category of compact quantum groups --for example de case of extensions, of Drinfeld twists, of matched pairs, of extensions, of linked pairs and of cocycle Singer…

Quantum Algebra · Mathematics 2013-09-26 Andrés Abella , Walter Ferrer Santos , Mariana Haim

We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…

Group Theory · Mathematics 2024-03-01 Francesco G. Russo , Olwethu Waka

We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group $N$, there is a one-to-one correspondence between the set of isomorphism classes of connected Lie…

Differential Geometry · Mathematics 2007-05-23 Hiroshi Tamaru , Hisashi Yoshida

Ehrenborg and Jung recently related the order complex for the lattice of d-divisible partitions with the simplicial complex of pointed ordered set partitions via a homotopy equivalence. The latter has top homology naturally identified as a…

Combinatorics · Mathematics 2011-11-17 Alexander Miller

We examine two classes of examples of Hausdorff \'etale factor groupoids; one comes from taking a quotient space of the unit space of an AF-groupoid, and the other comes from certain nonhomogeneous extensions of Cantor minimal systems…

Operator Algebras · Mathematics 2023-05-02 Mitch Haslehurst

We conjecture that the automorphism group of a topological parallelism on real projective 3-space is compact. We prove that at least the identity component of this group is, indeed, compact.

Geometric Topology · Mathematics 2017-10-17 Dieter Betten , Rainer Löwen

In this paper we present a construction for the compact form of the exceptional Lie group E6 by exponentiating the corresponding Lie algebra e6, which we realize as the the sum of f4, the derivations of the exceptional Jordan algebra J3 of…

Mathematical Physics · Physics 2008-11-26 Fabio Bernardoni , Sergio L. Cacciatori , Bianca L. Cerchiai , Antonio Scotti

We show that any compact quantum group having the same fusion rules as the ones of $SO(3)$ is the quantum automorphism group of a pair $(A, \varphi)$, where $A$ is a finite dimensional $C^*$-algebra endowed with a homogeneous faithful…

Quantum Algebra · Mathematics 2014-01-07 Colin Mrozinski

We show that closed, connected 4-manifolds up to connected sum with copies of the complex projective plane are classified in terms of the fundamental group, the orientation character and an extension class involving the second homotopy…

Geometric Topology · Mathematics 2023-04-13 Daniel Kasprowski , Mark Powell , Peter Teichner

It is well known in the literature that the momentum space associated to the $\kappa$-Poincar\'e algebra is described by the Lie group $\mathsf{A}\mathsf{N}(3)$. In this letter we show that the full $\kappa$-Poincar\'e Hopf algebra…

High Energy Physics - Theory · Physics 2022-11-03 Michele Arzano , Jerzy Kowalski-Glikman

We study analogues of Cartan decompositions of Lie groups for totally disconnected locally compact groups. It is shown using these decompositions that a large class of totally disconnected locally compact groups acting on trees and…

Group Theory · Mathematics 2025-03-28 Max Carter , George A. Willis

We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact…

Group Theory · Mathematics 2021-02-08 Jun Yu

(1) Every infinite, Abelian compact (Hausdorff) group K admits 2^|K|-many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact. (2) Every infinite Abelian group G admits a…

General Topology · Mathematics 2013-10-09 W. W. Comfort , S. U. Raczkowski , F. J. Trigos-Arrieta